Depends on whether or not moving the Balrog into the Diplomat Pixies is considered an attack by the race controlling the Balrog. Diplomat protects against attacks and the active use of racial or special powers. We've interpreted that to mean it stops your opponent of choice from using anything against you that actively targets one of your territories... including the use of relics and popular places.
If Diplomat Pixies can successfully negotiate a treaty prohibiting hostile acts by another race against them, you'd think something like that race's pet Balrog would be included under the list of "Things you Keep to Yourselves".